The 9 numbers and 7 Xs of the set (1,2,3,4,5,6,7,8,9,X,X,X,X,X,X,X ) were placed in a 4x4 grid to create a matrix as follows:
X 4 8 9
5 6 X 7
1 X X X
3 2 X X
Consider the Xs as black squares in a crossword and evaluate the sum of the sums taken per row: Sr=489+(56+7)+1+32=585.
Same operation per column: Sc= 513+(46+2)+8+97=666
Evaluate the ratio r= Sr/ Sc=585/666= 0.878378...

Your task :
Distribute the 9 non-zero digits and 7 black squares in a 4x4 grid so that
the ratio r, calculated as in the example above will be as close to the value of pi (=3.14159265…) as possible.

355/113 is a good approximation to pi, so if you could get the totals to be these two, you've got a good approximation, 3.141592920353983.

333/106, the previous level in a continued fraction approximation, is not as good, 3.141509433962264.

Of course multiples of the numerator and denominator of each of these, such as 710/226, would be the same good approximations.

Combining the two numerators and two denominators can give good approximations also. For example, the worst approximation shown below, 3.14160263 which is 2862/911, is (9*355+1*333)/(9*113+1*106). All are shown reduced to simplest form.